The vote was 277-130 to pass the bill.
"The goodwill of the American people is unmatched, and we should do everything we can to encourage Americans to give more, enabling charities, nonprofits, foundations and schools across the country to expand their reach and serve those most in need," said Rep. Dave Camp, R-Mich., chairman of the House Ways and Means Committee.
Sue Santa of the Council on Foundations said the bill "could strengthen charitable giving and give certainty to both donors and to the foundations."
The bill now goes to the Senate, where it is likely to get caught up in a debate over how to deal with a package of temporary tax breaks that expired at the beginning of the year. More than 50 temporary tax breaks expired in January, including several provisions in the bill passed Thursday.
The Republican-led House has voted to make a handful of them permanent, leaving the fate of others uncertain.
The Democratic-controlled Senate is taking a different approach. Instead of making them permanent, senators have been working on a package that would extend nearly all the temporary tax breaks through 2015.
The impasse is likely to last until after congressional elections in November.
The provision to benefit late donors has been popular as a way to boost donations for natural disasters that happen around the beginning of the year. In 2010, Congress extended the deadline to donate to relief efforts for earthquakes in both Haiti and Chile.
Under current law, donations must be made by Dec. 31 for taxpayers to claim the deduction on that year's tax return. Santa said extending the deadline to donate until April 15 would provide a natural time for donors to give — when they are filling out their tax forms.
The provision would save taxpayers $2.8 billion over the next decade, according to the Joint Committee on Taxation, the official tax scorekeeper for Congress.
The biggest tax break in Thursday's bill affects donations from individual retirement accounts. If you have an IRA, you must start taking minimum distributions six months after you turn 70. The amount depends on your age and the amount of money in your IRA.
For traditional IRAs, those distributions are taxable.
A temporary tax break that expired in January allowed seniors to avoid paying taxes on those distributions by donating them to charity. The bill passed Thursday would renew the tax beak and make it permanent.
The exemption is capped at $100,000 a year.
The tax break is popular among seniors with the means to make donations, Santa said. It would save them $8.4 billion over the next decade, according to the Joint Committee on Taxation.